results from the b-factories - particle physicspprc.qmul.ac.uk/~bevan/helmholtz/lecture1.pdf ·...
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August 2008 Adrian Bevan 1
Results from the B-factories(Lecture 1)
Adrian Bevan
Helmholz International Summer SchoolHEAVY QUARK PHYSICS
Bogoliubov Laboratory of Theoretical Physics,Dubna, Russia, August 11-21, 2008
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August 2008 Adrian Bevan 2
OutlineThese lectures will cover:
• Introduction– The B factories– CKM, mixing, and measuring CP asymmetries
• Unitarity triangle physics– CP violation measurements
• The angles: (α, β, γ) = (φ1, φ2, φ3)• Direct CP violation• Searching for new physics
– Side measurements• Vub and Vcb
• Measurements of b→dγ processes (related to |Vtd| / |Vts|)
• Tests of CPT• B →VV decays
– Testing SM calculations and searching for new physics
• Bostjan Golob will discuss charm physics, mixing, spectroscopy and other new physics searches from the B-factories.
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August 2008 Adrian Bevan 3
Notes• The B factories have produced many excellent results.
– Rather than show the results for both experiments for each measurement, I have selected results from either BaBar or Belle.
– Where possible I show world average results based on the latest measurements.
– I choose to use the α, β, γ convention for the Unitarity triangle angle measurements, and the S, C convention for time-dependent CP asymmetry measurements.
– Experimental references are listed at the end of each lecture.
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August 2008 Adrian Bevan 4
The B factories• 1964:
– Christensen, Cronin, Fitch and Turlay discover CP violation.
• 1967:– A. Sakharov: 3 conditions required to generate a baryon asymmetry:
• Period of departure from thermal equilibrium in the early universe.• Baryon number violation.• C and CP violation.
• 1981:– I. Bigi and A. Sanda propose measuring CP violation in B→ J/ψK0 decays.
• 1987:– P. Oddone realizes how to measure CP violation: convert the PEP ring into an
asymmetric energy e+e- collider.
• 1999:– BaBar and Belle start to take data. By 2001 CP violation has been established
(and confirmed) by measuring sin2β ≠0 in B→ J/ψK0 decays.BaBar Collaboration, PRL 87, 091801 (2001);Belle Collaboration, PRL 87, 091802 (2001).
Detector Considerations P. Oddone (LBL, Berkeley) . 1987In the Proceedings of Workshop on Conceptual Design of a Test Linear Collider: Possibilities for a B Anti-B Factory, Los Angeles, California, 26-30 Jan 1987, pp 423-446.
I. Bigi and A. Sanda Nucl.Phys.B193 p85 (1981)
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August 2008 Adrian Bevan 5
How do we make B mesons?• Collide electrons and positrons
at √s=10.58 GeV/c2
many types of interaction occur.
• We’re interested in (for B physics).
• Where
9.44 9.46
Mass (GeV/c2)
0
5
10
15
20
25
σ (e
+e- →
Had
rons
)(nb
) ϒ(1S)
10.00 10.020
5
10
15
20
25
ϒ(2S)
10.34 10.370
5
10
15
20
25
ϒ(3S)
10.54 10.58 10.620
5
10
15
20
25
ϒ(4S)
Υ(4S)off-peak
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August 2008 Adrian Bevan 6
PEP-II and KEKB
PEP-II• 9GeV e- on 3.1GeV e+
• Υ(4S) boost: βγ=0.56
KEKB• 8GeV e- on 3.5GeV e+
• Υ(4S) boost: βγ=0.425
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August 2008 Adrian Bevan 7
BABAR and Belle
BABAR
The differences between the two detectors are small. Both have:
• Asymmetric design.• Central tracking system• Particle Identification System• Electromagnetic Calorimeter• Solenoid Magnet• Muon/K0
L Detection System• High operation efficiency
DCH
DIRC
EMCIFR
SOLENOID
e−
e+
SVT
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August 2008 Adrian Bevan 8
What does an event look like?
π0
π0
0 0 0 eventB π π→
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August 2008 Adrian Bevan 9
Data
• Many Interactions produce B meson pairs:
0 0 and producedin equal quantitiesB B B B+ − Both experiments have recorded data while scanning
through the region above the Y(4S)
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August 2008 Adrian Bevan 10
The CKM matrix• Quarks change type in weak interactions:
• We parameterise the couplings Vij in the CKM matrix:
• At the B factories we want to measure:
32
2 2
23
4
(1 / 2 )
(1 1)1 / 2 ( )
A i
iV A
AAO
λ ρ η
λ
λ
λρλ λ
η
λλ λ
⎛ ⎞−⎜ ⎟
= − − +⎜ ⎟⎜ ⎟−⎝ ⎠
−
− −
~ 0.22~ 0.8~ 0.2 0.27~ 0.28 0.37
Aλ
ρη
−−
V =, ,iq u c t=
, ,jq d s b=
W +
ijV
2 2(1 / 2), (1 / 2)ρ ρ λ η η λ≈ − ≈ −
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August 2008 Adrian Bevan 11
Mixing• Neutral B mesons oscillate between B0 and B0, The Hamiltonian is
• We study the mass eigenstates:– If CPT is conserved z=0– p and q are mixing parameters:
– Physics depends on mass eigenstate differences in m and Γ:
– Δ Γ / Γ = -0.003 (usually set ΔΓ = 0).
= + Long Distance TermsW− W+
u, c, t
u, c, t
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August 2008 Adrian Bevan 12
Time-dependent CP asymmetries• Ingredients of a time-dependent CP asymmetry measurement:
– Isolate interesting signal B decay: BREC.– Identify the flavour of the non-signal B meson (BTAG) at the time it
decays.– Measure the spatial separation between the decay vertices of both B
mesons: convert to a proper time difference Δt = Δz / βγc; fit for S and C.• The time evolution of BTAG = B0(B0) is
• S is related to CP violation in the interference between mixing and decay.
• C is related to direct CP violation.
• ηf is the CP eigenvalue of BREC.
Note that Belle use a convention where C is replaced by ACP = −C
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August 2008 Adrian Bevan 13
Time-dependent CP asymmetries• Ingredients of a time-dependent CP asymmetry measurement:
– Isolate interesting signal B decay: BREC.– Identify the flavour of the non-signal B meson (BTAG) at the time it
decays.– Measure the spatial separation between the decay vertices of both B
mesons: convert to a proper time difference Δt = Δz / βγc; fit for S and C.• The time evolution of BTAG = B0(B0) is Note that Belle use a convention
where C is replaced by ACP = −C
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August 2008 Adrian Bevan 14
Time-dependent CP asymmetries• Construct an asymmetry as a function of Δt:
Δt (ps)Δt (ps)
f+(Δt)f-(Δt)
Experimental effects we need to include:• Detector resolution on Δt.• Dilution from flavor tagging (see later).
With detector resolution With detector resolution and dilution
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August 2008 Adrian Bevan 15
Time integrated CP asymmetries• Charged B mesons do not oscillate.• Measure a direct CP asymmetry by comparing amplitudes of decay:
• Event counting exercise! • With two (or more) amplitudes
see that we need different weak and strong phases to generate.
• ACP is largest when a1 = a2.
• Need to measure δ!
• We can use this technique when studying neutral B mesons decaying to a self tagging final state.
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August 2008 Adrian Bevan 16
Isolating signal events• Beam energy is known very well at an e+e− collider
– use an energy difference and effective mass to select events:
MES σ ~ 3 MeV
B background
signal
σ(ΔE)~ 15-80 MeV (mode dependent)
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August 2008 Adrian Bevan 17
More background suppression• Use the shape of an event to distinguish between Υ(4S)→BB and
e+e− → qq.• √s=10.58 GeV: compare mBB = 10.56 GeV/c2 with
– muu, mdd, mss ~ few to 100 MeV/c2
– mcc ~ 1.25 GeV/c2
B-pair events decay isotropically continuum (ee→qq) eventsare ‘jetty’
Analyses combine several event shape variables in a single discriminating variable: either Fisher or artificial Neural Network.
This allows for some discrimination between B and continuum events
Signal
u,d,s,cbackground
Fisher Discriminant:
Arb
itrar
y U
nits
i ii
F xα= ∑
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August 2008 Adrian Bevan 18
Measuring Δt
Asymmetric energiesproduce boosted Υ(4S), decaying into coherent BB pair
e- e+
B0
B0
Fully reconstruct decay to state or admixture under study (BREC)
π+
π−
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August 2008 Adrian Bevan 19
Measuring Δt
Asymmetric energiesproduce boosted Υ(4S), decaying into coherent BB pair
e- e+
B0
B0
Determine time between decays from vertices
Δz=(βγc)Δt
Fully reconstruct decay to state or admixture under study (BREC)
π+
π−
• βγ = 0.56 (BaBar)= 0.425 (Belle)
• t = t1 corresponds to the time that BTAG decays.
• t2-t1= Δtt=t1t=t2
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August 2008 Adrian Bevan 20
Measuring Δt
• Then fit the Δt distribution to determine the amplitude of sine and cosine terms.
Asymmetric energiesproduce boosted Υ(4S), decaying into coherent BB pair
Determine flavor and vertex position of other B decay (BTAG)
l-
K-
e- e+
B0
B0
Determine time between decays from vertices
Δz=(βγc)Δt
Fully reconstruct decay to state or admixture under study (BREC)
π+
π−
• βγ = 0.56 (BaBar)= 0.425 (Belle)
• t = t1 corresponds to the time that BTAG decays.
• t2-t1= Δtt=t1t=t2
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August 2008 Adrian Bevan 21
Flavor tagging
0B0B
• Decay products of BTAG are used to determine its flavor.
• At Δt=0, the flavor of BREC is opposite to that of other BTAG.
• BREC continues to mix until it decays.
• Different BTAG final states have different purities and different mis-tag probabilities.
• Can (right) split information by physical category or (below) use a continuous variable to distinguish particle and anti-particle.
Lepton
Kaon 1
Kaon 2 Kaon-Pion
Pion Other
BaBar’s flavor tagging algorithm splits events into mutually exclusive categories ranked by signal purity and mis-tag probability. Belle opt to use a continuous variable output. These plots are for the 316fb-1 h+h- data sample.
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August 2008 Adrian Bevan 22
Flavor tagging• Don’t always identify BTAG flavor correctly: asymmetry diluted by
• ω is probability for assigning the wrong flavor (mistag probability).• Effect is slightly different for B0 and B0 tags: Δω• Define an effective tagging efficiency:
• Use a modified f±(Δt):
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August 2008 Adrian Bevan 23
Flavor tagging• Don’t always identify BTAG flavor correctly: asymmetry diluted by
• ω is probability for assigning the wrong flavor (mistag probability).• Effect is slightly different for B0 and B0 tags: Δω• Define an effective tagging efficiency:
• Use a modified f±(Δt):
Example: The BaBar tagging algorithm:
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August 2008 Adrian Bevan 24
Fitting for CP asymmetries• Perform an extended un-binned ML fit in several dimensions (2 to 8).
– P ji is the probability density functions for the ith event and jth component
(type) of event.– nj is the event yield of the jth component.– N is the total number of events.– Usually replicate the likelihood for each tagging category (BaBar) or
include a variable in the fit that incorporates flavor tagging information (Belle).
• In practice we minimize –lnL in order to obtain the most probable value of our experimental observables with a 68.3% confidence level (1σ error) using MINUIT.
• S and C (or ACP) are observables that are allowed to vary when we fit the data.
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August 2008 Adrian Bevan 25
Angles of the Unitarity triangle
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August 2008 Adrian Bevan 26
0 0
0 0
0 0
0 01
0 0
0 *0
/
/
(2 )
/
L
S
S
c S
c S
b ccsB J K
B J K
B S K
B K
B K
B J K
ψ
ψ
ψ
χ
η
ψ
→
→
→
→
→
→
→
0
(*) (*)
0
0
0
0 0
(*)0
0
0 0
/
(980)
B JB D DB KB KB KB KB KB KKKB f K
ψπ
η
ρ
ω
π
φ
+ −
→
→
′→
→
→
→
→
→
→
Theoretically clean (SM uncertainties ~10-2 to 10-3) tree dominated decays to Charmonium + K0 final states.
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August 2008 Adrian Bevan 27
CP violation: β• Need to determine many parameters before we can extract S and C
(and the angles of the triangle):– ω, Δω, εTAG, ΔεTAG for signal and for background.– Use a sample of fully reconstructed B decays to flavor specific final
states to determine these parameters (Bflav).– Sample includes:
0 (*)
0 (*)
0 (*)1
0 *0 *0/ , Background
B DB DB D a
B J K K K
π
ρ
ψ π
− +
− +
− +
+ −
→
→
→
→ →
D−
π+
π−π+π−
BREC=BFLAV
BTAG
Lepton, pion or kaon
νThis method to validate the tagging performance is used for all time-dependent CP asymmetry measurements.
BaBar sin2β analysis
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August 2008 Adrian Bevan 28
CP violation: β• Measure S and C in several modes.
• Theoretically clean: Tree level process dominates:
• Gluonic loop (penguin) is small:
• Calculations suggest C<10-3.
• Data driven methods constrain C<0.012.
b ccs→
1fη = +
1fη = −
~ 0.5efffη
This mode is a CP admixture with CP even and odd parts that need to be distinguished using an angular analysis.
b
d
d
−W cc
s
0B ψ/J0K
0K0Bb
d−W
s
d
cc
g
u,c,t
ψ/J
BaBar sin2β analysis
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August 2008 Adrian Bevan 29
CP violation: β• CP violating asymmetry is well established in these decays!
1fη = +
1fη = −
BaBar Collaboration, SLAC-PUB-13317, PRL 99, 171803 (2007)
BaBar sin2β analysis
1998
2000
2000
2001
2008
sin 2 0.671 0.024β = ±
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August 2008 Adrian Bevan 30
CP violation: β
0 0
0 0
0 0
0 01
0 0
0 *0
/
/
(2 )
/
L
S
S
c S
c S
B J K
B J K
B S K
B K
B K
B J K
ψ
ψ
ψ
χ
η
ψ
→
→
→
→
→
→
• Theoretically clean CP violation measurements consistent with the Standard Model for:
• Established technique for extracting S and C that can be used for other final sates.
• Measured S=sin2 β provides a reference point to search for New Physics (NP).
• Four solutions exist in the ρ-η plane as we compute arcsin(2β).
• Additional measurements provide cos(2β) and help to resolve ambiguities.
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August 2008 Adrian Bevan 31
b uudBBB
ππρπρρ
→→→→
1
1
1
1
1 1
B aB aB bB bB a a
πρπρ
→→→→→
b→uud transitions with possible loop contributions. Extract α using• SU(2) Isospin relations.• SU(3) flavour related processes.
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August 2008 Adrian Bevan 32
CP violation: α• Interference between box and tree results in an asymmetry that is
sensitive to α in B→hh decays: h=π, ρ, …• Loop corrections are not negligible for α.
• Measure S ∝αeff.• Need to determine δα=αeff-α [ P/T is different for each final state ]
:tdV β
* :tdV β
:ubV γ
+Loops (penguins)
0sin(2 )
hh
hh
CS α
=
=
2eff
sin( )
1 sin(2 )hh
hh hh
P T
C
S C
δ
αδ δ δ
∝
= −
= −
• This scenario is equivalent to the measurement of sin2β in Charmonium decays … but nature is more complicated than this!
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August 2008 Adrian Bevan 33
CP violation: α• Interference between box and tree results in an asymmetry that is
sensitive to α in B→hh decays: h=π, ρ, …• Loop corrections are not negligible for α.
• Measure Shh ∝αeff.• Need to determine δα=αeff-α [ P/T is different for each final state ]
:tdV β
* :tdV β
:ubV γ
+Loops (penguins)
0sin(2 )
hh
hh
CS α
=
=
2eff
sin( )
1 sin(2 )hh
hh hh
P T
C
S C
δ
αδ δ δ
∝
= −
= −
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August 2008 Adrian Bevan 34
Bounding penguins• Several recipes describe how to bound penguins and measure
alpha.– These are based on SU(2) or SU(3) symmetry.
SU(2)(Isospin analysis)
π+π− and ρ+ρ−
Gronau-LondonIsospin Triangles
π+ / − ρ− / +
Lipkin (et al.)Isospin Pentagons
• Use charged and neutral B decays to the hh final state to constrain the penguin contribution and measure alpha.
• Use charged and neutral B decays to the ρπ final state to constrain the penguin contribution and measure alpha. Remove any overlapping regions in the Dalitz plot.
π+ / − π − / + π0
Snider-Quinn (et al.)Fit Dalitz plot and extract parameters related to α
• Regions of the Dalitz plot with intersecting ρ bands are included in this analysis; this helps resolve ambiguities.
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August 2008 Adrian Bevan 35
Bounding penguins• Several recipes describe how to bound penguins and measure
alpha.– These are based on SU(2) or SU(3) symmetry.
SU(3)flavor analysis
Fit for T and P amplitudes, as well as phase differences
δTP in related decays
• Theoretical uncertainties tend to result in weaker constraints than the SU(2) analyses.
• No choice for decays like B→a1π.
• Exception exists for B→ρ+ρ−: Use K*0ρ+ to constrain penguin contribution in ρ+ρ− and measure α with better precision than SU(2).
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August 2008 Adrian Bevan 36
Isospin analysis• Consider the simplest case: B→ππ / ρρ decays.
• There are SU(2) violating corrections to consider, for example electroweak penguins, but these are much smaller than current experimental accuracy and can be incorporated into the Isospin analysis.
δα
δα = αeff-α
0
0 0 0
0
( ) . .( ) . .( ) . .
h h
B h h C CB h h C CB h h C C
S + −
+ −
+ +
→ +
→ +
→ +
BBB
For ππ & ρρ require:
00 0
00 0
12
12
A A A
A A A
+− +
+− +
+ =
+ =
Measuring S in h0h0
provides an additional constraint on this angle.
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August 2008 Adrian Bevan 37
Belle π0π0 0 taggedB
0 taggedB
B→ππ• Easy to isolate signal for π+π− and π+π0 as these modes are
relatively clean and have large B ~ O(5 ×10−6).
• Much harder to isolate π0π0: B ~ 1.5×10−6
– No tracks in the final state to provide vertex information.– Have to reconstruct B0→π0π0→ γγγγ, which has a large ΔE resolution.
• Possible to separate flavor tags tomeasure C00. This information completes the set of informationrequired for an Isospin analysis.
Belle π+π−
Belle π+π−
0 taggedB0 taggedB
0.65 0.07
0.38 0.06
S
Cπ π
π π
+ −
+ −
= − ±
= − ±
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August 2008 Adrian Bevan 38
B→ππ• Inputs from:
How do I read plots like this?
• 1-CL = 1: central value reported from measurements, before considering uncertainties.
• 1-CL = 0: Region excluded by experiment.
• If we think in terms of Gaussian errors, then 1-CL = 0.317, 0.046, 0.003 correspond to regions allowed at 1σ, 2σ and 3σ.
Gronau-London Isospin analysis0
0
0 0 0
BBB
π π
π π
π π
+ −
+ +
→
→
→
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August 2008 Adrian Bevan 39
B→ππ
How do I read plots like this?
• At 68.3% CL = 1σ for Gaussian errors we have the following allowed regions for α:
7.582.5 103.1118.0 152.4
166.7
α
α
α
α
°
°
°
°
<
< <
< <
>
Gronau-London Isospin analysis
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August 2008 Adrian Bevan 40
B→ππ• If we have measured CP violation in B→π+π−, does this tell us
something about α?
• Yes!• CP violation measured as a non-
zero value of S is related to α via:
Cππ ≠ 0 gives a scale factor.
Sππ ≠ 0 means there is CP violation in this decay and sin(2αeff) ≠0.
If α=0, then the unitaritytriangle would be flat, so if S≠0 we must have α≠0.
Can use constraints on P from Bs→K+K− to remove the solutions near α=0° and 180°.
Excluded usingAdditionalinformation.
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August 2008 Adrian Bevan 41
B→ρρ• This is a decay of a B meson to two vector mesons.• Requires a (simplified) angular analysis (will come back to this in Lecture 2).• Inputs from:
• fL ~ 1 for B→ρρ decays: this helps simplify extracting α.• Can measure S00 as well as C00 to help resolve ambiguities.• Finite width of the ρ is ignored in the α determination (see Falk et al.)
• We define the fraction of longitudinally polarised events as:
0
0
0 0 0
BBB
ρ ρ
ρ ρ
ρ ρ
+ −
+ +
→
→
→
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August 2008 Adrian Bevan 42
B→ρρ• Obtain a more stringent constraint on α than from B→ππ decays.
BaBar ρ0ρ0 paper
• Not including S00 and C00.• Include C00, but not S00.• Using all constraints.
Some features of this result:
• Two of the solutions overlap near 90°and 180°.
• Using S00 and C00 we see that the solution at 80° is very slightly preferred over the other solutions.
• There are two regions for α that are excluded:
45130
α
α
≠
≠
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August 2008 Adrian Bevan 43
Using SU(3)• Can relate the penguin contribution in K*+ρ0 to that in ρ+ρ−:
0.9 0.6F = ±
• If we assume that |δTP| < 90°:
• Relaxing this assumption:
• Most precise determination of α!
|δTP| > 90°|δTP| < 90°
BaBar ρ+ρ− paper
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August 2008 Adrian Bevan 44
B→ρπ (π+π−π0 Dalitz Plot)• Analyse a transformed Dalitz Plot to extract parameters related to α.• Use the Snyder-Quinn method.
• Fit the time-dependence of the amplitudes in the Dalitz plot:
• 26 parameters: Bi-linear form factor coefficients: U’s and I’s.
ρ+ π−
ρ 0π 0
ρ−π+
(m0=mπ+π-)
(θ0=
π+ π-he
licity
)
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August 2008 Adrian Bevan 45
B→ρπ (π+π−π0 Dalitz Plot)• The amplitudes are written in terms of Us and Is:
• Which are related to CP conserving and CP violating observables:
CP conservingobservables
CP violatingobservables
Some features of this result:
• No region is excluded at 3σ significance.
• A high statistics measurement will help resolve ambiguities in the measured value of α.
• Results from the Dalitz analysis, and the pentagon analysis (solid) are more stringent than using the Dalitz analysis alone.
Belle ρ+π− paper
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August 2008 Adrian Bevan 46
CP violation: α• No single mode dominates our knowledge of α.
– Three comparable inputs from ππ, ρρ, ρπ using SU(2).– SU(3) can be used to provide a more stringent constraint for α from
ρ+ρ−.• Many modes are required
to try and measure αprecisely. Any deviation in measured values of could indicate new physics.
0 0 0
0 0 0
0
1
1
, ,, ,
...
BBBB aB a
π π π π π π
ρ ρ ρ ρ ρ ρ
π π ππρ
+ − +
+ − +
+ −
→
→
→→→
Show
n he
re
Not shown: Need more data than currently available, and use SU(3) to extract α from final states with axial-vector mesons. These are related to hh modes above.
6.2 7.0(2) 5.3 (3) 6.497.5 89.8SU SUα α+ +
− −= =
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August 2008 Adrian Bevan 47
(*) (*)
0
0 (*)
0 (*)
0
interfering with b c b uB D KBB DB D
charml s
D K
es
π
ρ
π− +
→
→+
→ →
→
→
Extract γ using B→D(*)K(*) final states using:• GLW: Use CP eigen-states of D0.• ADS: Interference between doubly suppressed decays.• GGSZ: Use the Dalitz structure of D→Ksh+h− decays.
Measurements using neutral D mesons ignore D mixing.
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August 2008 Adrian Bevan 48
γ: GLW Method• GLW Method: Study and• X+ is a strangeness one meson e.g. a K+ or K*+.• is a CP eigenstate (use these to extract γ):
• The precision on γ is strongly dependent on the value of rB.– rB~0.1 as this is a ratio of Cabibbo suppressed to Cabibbo allowed
decays and also includes a color suppression factor for B+→D(*)K(*) b→udecays.
• Measurement has an 8-fold ambiguity on γ.
Gronau, London, Wyler, PLB253 p483 (1991).
0CPB D X+ +→ ( )0 0. . B D X C C D K π+ + + −→ + →
0CPD
01
0 0 0 0 01
,
, ,CP
CP S S S
D K K
D K K K
π π
π ω φ
+ − − +=+
=−
=
=0 0
20 0
( ) ( )2 1 2 cos cos( ) ( )
CP CPCP B B B
B D K B D KR r rB D K B D K
γ δ− − + +
± ±± − − + +
Γ → + Γ →= = + ±
Γ → + Γ →0 0
0 0
( ) ( ) 2 sin sin( ) ( )
CP CP B BCP
CP
B D K B D K rAB D K B D K R
δγ− − + +± ±
± − − + +±
Γ → − Γ →= = ±
Γ → + Γ →
• 4 observables• 3 unknowns:
rB, γ and δ
cos cos0.23 0.97sin sin 0.23 0.23
cs c
cd c
VV
θθ
∝ = =∝ = =
Cabbibo allowed
Cabbibo suppressed
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August 2008 Adrian Bevan 49
γ: GLW Method• Insufficient data to constrain γ:
• x± is related to RCP± and ACP±.
BaBar GLW paper
149±16
90±13
106±14
129±15
• We can perform similar measurements using D*CPK:
• Again: insufficient statistics to perform a precision measurement of γ.
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August 2008 Adrian Bevan 50
γ: GLW Method21 2 cos cosCP B B BR r r γ δ± = + ±2 sin sinB B
CPCP
rAR
γ δ±
±
= ±
• All measured ACP and RCP values are compatible with 0 and 1, respectively.
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August 2008 Adrian Bevan 51
γ: ADS Method• ADS Method: Study• Reconstruct doubly suppressed decays with common final states
and extract γ through interference between these amplitudes:
• γ extracted using ratios of rates:
,0 *0 *B D K± ±→
Attwood, Dunietz, Soni, PRL 78 3257 (1997)
Vcb
VusVub
Vcs
(*)0 (*)B D K− −→ (*)0 (*)B D K− −→CKM and Color SuppressedCKM Favoured
(*) (*)2 2 (*) (*)2 cos cosB D B DR r r r r γ δ= + +(*)0(*)
(*)0
0
0
( )( )
( )( )
B
D
A B D KrA B D K
A D KrA D K
ππ
− −
− −
+ −
− +
→=
→
→=
→
• δ(*) = δ(*)B + δD
• δ(*) is the sum of strong phase differences between the two B and D decay amplitudes.
• rD and rB are measured in B and charm factories.
• δD is measured by CLEO-c
u
d(*)0D K π+ −→CKM FavouredD(*)0 K+
π−
W−
c s
u u
Vcs
Vud
(*)0D K π+ −→Doubly CKM Suppressed D(*)0 π−
K+
W+
c d
u u
s
u
Vus
Vcd
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August 2008 Adrian Bevan 52
γ: ADS Method(*) (*)2 2 (*) (*)2 cos cosB D B DR r r r r γ δ= + +
• Insufficient precision to extract γusing the ADS method alone.
• Measurement of RADS can be used to constrain rB.
Help when extracting γ using other methods.
• Full statistics from the B factories will not improve the situation significantly.
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August 2008 Adrian Bevan 53
γ: GGSZ Method• GGSZ (“Dalitz”) Method: Study D(*)0K(*) using the D(*)0→Ksh+h− Dalitz
structure to constrain γ. (h = π, K)– Self tagging: use charge for B± decays or K(*) flavour for B0 mesons.
where
– Need a detailed model of the amplitudes in the D meson Dalitz plot.
Giri, Grossman, Soffer, Zupan, PRD 68, 054018 (2003)
( )0 2 2 2 2( , ) ,( ( )( ) ) BS D
iBf mA B K h h mK em f m r δ γ±
+±+
−−
− +±→ ∝ +
0SK h
m m ±± =
• Use a control sample (CLEO-c data or D*+→D0π+) to measure the Dalitz plot.
π+π− K+K−
Control sample plots from BaBar GGSZ paper
* 0D D π+ −→
0 0SD K h h+ −→
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August 2008 Adrian Bevan 54
γ: GGSZ Method
Belle GGSZ paper
• Note: axes swapped between Figures (a) and (b).
• Differences between the two plots contain information on γ.
• Method has a 2-fold ambiguity on γ.
B DK+ +→ B DK− −→
( )( )
1213 stat syst model
2324 stat syst model
76 4 9
76 5 5
Belle
BaBar
γ
γ
+−
+−
= ± ±
= ± ±
• rB ~0.16 (Belle), and ~0.09 (BaBar)
• The Belle measurement has a larger value for rB, hence a smaller uncertainty on γ.
BaBar GGSZ paper
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August 2008 Adrian Bevan 55
CP violation: γ• As with α, no single channel dominates the determination of γ.
– Several methods available. Best results come from the GGSZ Dalitz method.– LHCb will produce more precise analyses of these decay modes, and will also be
able to use U-spin related rare charmless decays to try and measure γ more precisely.
• The B factories have started to measure γ! • With β measured to ~1°, and α measured to ~7°, we can use γ measurements to over-constrain the Unitarity triangle and test the integrity of the CKM mechanism.
• The CKM mechanism works at this level:
• New experiments are needed to test the CKM to a higher accuracy: LHCb, SuperB, and SuperKEKB.
( )180 10 21α β γ+ + − = ±
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August 2008 Adrian Bevan 56
Next Lecture• Direct CP Violation.
• CP violation: Searching for new physics.
• Summary of CP violation signals found.
• Side measurements.
• B→VV decays.
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August 2008 Adrian Bevan 57
Experimental References• Experiments Averages
• β
• α
• γ
ππ ρρ
ρπ
b ccs→
GGSZ ADS
GLW